JK uses a modified Quake engine, right? So far I've been able to make every game that uses any of the Quake engines feel totally smooth by using vsync and running the game with constant 60fps (I'm using a TFT). JK, however, feels extremely choppy and everything else but smooth. How can I make the game display my the current fps so I can check whether it is running with constant 60fps or not?

JK uses its own Lucasarts in-house engine, called the Sith Engine IIRC. It does not use the quake engine (Jedi Outcast and Jedi Academy do use the Quake 3 engine however). To see your FPS while ingame, press T and type "framerate" (without the quotation marks) and enter.

It is an odd engine. While the PC I'm running it on is overkill for such an old game and I get 85 fps with the engine, I've noticed that the instant I add any level of AA or AF the framerate drops to 30 fps. I can't quite figure that one out.